Rolling mill strip thickness controller

ABSTRACT

A method for automatically controlling the thickness of product emerging from a rolling mill. Signals indicative of total roll force (F), rollgap position (S), angular position of one mill roll (v) and downstream product thickness (h) are utilized to obtain an output signal indicative of roll eccentricity affecting the true instantaneous rollgap position as a function of the measured mill roll angular position. The output signal may be use to compensate an estimate of instantaneous thickness of the product for the purpose of controlling the gap between work rolls. If preferred the output signal may be further processed to obtain an output signal indicative of the periodic roll eccentricity of a set of rolls having a common period of rotation or of a plurality of such sets.

TECHNICAL FIELD

This invention relates to a method of, and apparatus for, control of arolling mill and more particularly to control of thickness on hot andcold metal rolling mills.

BACKGROUND ART

A common configuration of rolling mill has four or more rolls mounted ina vertical plane with two smaller diameter work rolls supported betweenlarger diameter back-up rolls. Such mills may operate in isolation or intandem with other similar mill stands.

A particular problem of importance in mill control arises from out-ofroundness in one or more of the rolls which produces cyclic variationsin the gap between the rolls. These variations in gap causecorresponding changes in roll separating force, metal velocities and,most importantly, in the thickness of the product issuing from betweenthe rolls.

Control of output product thickness is usually effected by changing therelative gap between the work rolls by means of a motor driven screw orhydraulic cylinder acting on the back-up roll bearings. Usually thebearing position is measured with respect to the support frame (theso-called "rollgap position"). The separation of the work rolls cannotbe directly measured by the roll gap position because of significantelastic deformations in the mill stand components.

It is conventional practice to provide a rolling mill stand with atransducer for measuring the total deformation force applied to theworkpiece and another for measuring the roll gap position.

Furthermore, it is often desirable to install a thickness measuringgauge after the stand to monitor the operation of the process and theeffectiveness of any thickness control system which may be installed.

It is well known to those skilled in this art that the dynamic responseof a feedback control system is deleteriously affected if a time delayoccurs between the creation of a change and measurement of the changeand for this reason techniques have been developed for estimating therolled strip thickness from a knowledge of the nominal gap between therolls and the change in this gap due to elastic deformations which arecalculated as a function of measured force and nominal material width.This "instantaneous" estimate of product thickness can be used forfeedback control to the stand on which measurements were obtained or forfeedforward control to downstream stands. Major benefits are gained byuse of this technique if the rollgap adjusting mechanism has a responsetime which is significantly less than the time delay to the measuredthickness obtained downstream.

A major drawback of the feedback and feedforward control techniquesdescribed above is that if the mill work rolls and backup rolls are notperfectly round, the measured rollgap position is not equal to the trueroll gap position, and eccentricity induced signal components appear inthe force and thickness measurements. These lead to an incorrect"estimated thickness" which results in the control systems correctingnon-existent errors, thereby creating worse product thickness deviationsthan are likely to arise with no control.

Numerous techniques have been proposed for overcoming this problemincluding tuned filters, adjustable deadbands, the addition of forcecontrol systems and direct measurement of the eccentricity effects asthe rolls rotate with subsequent subtraction to cancel their effect. Thelatter technique has been shown to have some beneficial results butsuffers from the need to install eccentricity measuring equipment on therolls producing the eccentricity component in the transducer signals.

Normally the back-up rolls are the major source of the eccentricitysignal components although the work rolls or other, intermediate rolls,may also contribute.

It is an object of the present invention to provide a simple andeffective method for eliminating the effect of multiple, superimposedcyclic variations caused by the individual roll eccentricity signals.The method proposed is capable of operation without direct measurementof the angular position of all the rolls. However, if such informationis available, it may be used in the proposed method to obtain furtherbenefits. Accurate, angular speed or position information is readilyavailable for the driven rolls, usually the work rolls in a four-highconfiguration. The angular position measurement is preferred to anintegrated speed measurement because of its inherently greater accuracy.These signals and a knowledge of all the roll diameters is sufficient toimplement the proposed method of roll eccentricity control.

DISCLOSURE OF THE INVENTION

According to one aspect, the invention consists of a method forautomatically controlling the thickness of product emerging from arolling stand comprising the steps of producing a first input signalindicative of total roll force, producing a second input signalindicative of rollgap position, producing a third input signalindicative of the angular position of a first mill roll, producing afourth input signal indicative of product thickness at a predetermineddownstream location relative to the rollgap and deriving from saidfirst, second, third and fourth input signals a first output signalindicative of the total roll eccentricity affecting the trueinstantaneous rollgap position as a function of the first mill rollangular position. This signal varies with time as the rolls rotate andthe relative phase and amplitude of the various roll eccentricitycomponents alters.

In preferred embodiments of the invention, the first output signal isfiltered by means employing an algorithm which requires an accurateknowledge of the period of each significant component which contributesto the roll eccentricity signal and produces a second output signalrepresenting the predicted composite roll eccentricity at the rollgap.

A further recommended step is to estimate the instantaneous productthickness from the first signal (F) and the second signal (S) and tomodify this thickness estimate by the second output signal, therebycompensating for the effect of roll eccentricity and producing aneccentricity compensated, instantaneous thickness estimate. This lattersignal is then used as the input signal to a feedback thicknesscontroller which adjusts the gap between the work rolls.

If the individual roll periods cannot be estimated directly from angularposition measurements or indirectly from roll diameter or speed ratiosand other roll angular position measurements, then adaptive techniquesshould be invoked to estimate the fundamental signal period for eachroll which is considered to be capable of producing eccentricity relatedthickness errors.

Further improvement in performance may be achieved by adding a suitablysynchronised proportion of the second output signal to the output of thefeedback thickness controller. This technique is not particularlydemanding to implement and enables the true actuator response to befully utilised for thickness control. For preference the control designincorporates other features which explicitly compensate for theinfluence of product dimensions, material properties, bearingcharacteristics, dependence of the time delays in the process uponrolling speed and variations in stand deformation behaviour.

According to a second aspect the invention consists in:

apparatus for controlling the thickness of material produced by arolling mill stand comprising;

means for producing a first input signal indicative of the roll force(F);

means for producing a second input signal indicative of rollgap position(S);

means for producing a third input signal indicative of roll angularposition (v);

means for producing a fourth input signal indicative of productthickness at a predetermined downstream position relative to the rollgap(h);

means for deriving from the first, second, third and fourth inputsignals a first output signal indicative of total roll eccentricities;

means for filtering the first output signal to minimise the influence ofnoise and produce a second output signal representing the predicted,composite roll eccentricity at the roll gap for all rolls whose periodsare specified by angular position or speed measurements or roll diameterinformation;

means for deriving from the first input and second input signal a thirdoutput signal indicative of instantaneous product thickness at therollgap, and

means for utilising the second output and third output signals to adjustthe rollgap position whereby to control product thickness independentlyof roll eccentricity disturbances.

If desired, a deadzone may be introduced to reduce the effect of anyunfiltered error components in the instantaneous thickness estimate.

An advantage of a preferred embodiment is its ability to compensate forany hysteresis which may arise due to sliding friction between movingparts of the stand components or hydraulic cylinders and pistons.

The method of the invention is made possible by the development of a neweccentricity estimation and filtering algorithm which may be implementedin a digital computer and applied to one or more stands in a rollingmill train.

BRIEF DESCRIPTION OF THE DRAWINGS

By way of example an embodiment of the invention is describedhereinafter with reference to the accompanying drawings wherein:

FIG. 1 shows schematically a conventional rolling mill stand and controlsystem.

FIG. 2 shows schematically an embodiment of a rolling mill controlsystem according to the invention.

FIG. 3 shows schematically a particular form of Control System structuretested by computer simulation.

FIG. 4 shows an Example of an eccentricity period estimation algorithmfor a case where the true period was 1.0 s.

FIG. 5 shows a filtering arrangement for multiple eccentric rolls withfour different periods.

FIG. 6 shows computer simulation results for nominal rolling conditionsfor the case of one periodic eccentricity.

FIG. 7 shows results corresponding to the previous figure when errorsexist in the mill modulus and plasticity parameters.

FIG. 8 shows controller simulation results for the case of fourdifferent roll diameters in a four-high mill, each containing a similareccentricity amplitude.

FIG. 9 shows results of application of an embodiment of the invention toa tandem mill.

BEST MODE OF PERFORMANCE

With reference to FIG. 1 there is shown schematically a conventionalmill stand having a frame 1, upper back up roll 2, upper work roll 3,lower work roll 4 and lower backup roll 5. The mill is driven by motors6.

Rollgap position controls hydraulic cylinders 7 which act on bearings 8of backup roll 5.

The mill is provided with a force transducer 9 producing a signalindicative of total roll force F' and a roll gap transducer producing aroll gap position signal S.

One or more roll angular position signals v are available fromtransducers associated with the drive system. Roll angular positionsignals (v₂ -v₄) may optionally be available for other rolls as well.Gauge 11 measures the thickness of strip 12 downstream of the work rollsand produces a thickness signal h'. Signals v, h', F' and S are fed to athickness controller, together with a reference thickness signal h*. Aroll gap actuator control signal is output by the thickness controllerand adjusts hydraulic cylinders 7 which act on backup roll bearings 8 tocontrol the gap between the work rolls.

An embodiment according to the invention is shown schematically in FIG.2. The same numerals and letters are used in FIG. 2 to identify partsand signals as were used in FIG. 1 to identify corresponding parts andsignals.

In FIG. 2, C₁ to C₄ represent conventional control algorithms. It willbe understood that in general signals may be processed via an algorithmby means of digital or analogue computing apparatus per se known in theart.

The mill stand of FIG. 2 provides signals F' (measured force), S(rollgap position), v (roll speed tachometer or position detector) andh' (downstream thickness) from suitable transducers or measuringinstruments.

The measurements are processed via a thickness estimator algorithm 13and an eccentricity predictor incorporating a smoothing filter 16. Setsof position synchronised measurements are analysed and the periodiccomponent obtained by a specified mathematical substitution.

The eccentricity predictor 16 produces a roll eccentricity estimatesignal 17 which is used by the thickness estimator 13 to produce acompensated thickness estimate signal h. This signal h and the measuredthickness signal h' are used in a conventional manner for feedbackcontrol. A further element is added via a feedforward controller C₄which uses the roll eccentricity estimate signal to make rollgapposition adjustments before an error is detectable.

A deadzone 18 may optionally be inserted to operate on the thicknesssignal h to filter out noise or other undesirable components which havenot been eliminated by the thickness estimator.

A variety of controll configurations of varying complexity may begenerated. Most simply this can be done by redefining the four differentcontrol algorithms C₁ to C₄ of FIG. 2.

Another feasible configuration could be generated by deleting therollgap position feedback signal to the rollgap position controller andchanging the settings of controllers C₁ to C₄ and the process gaincompensation function.

By way of further explanation, the strip exit thickness h, is given by:

    h=S(F,W)+(S-S.sub.0)+e                                     (1)

where S(F,W) is the elastic deformation of the stand components, W isthe strip width, S is the rollgap (or screw) position with respect to anarbitrary datum, S_(o) is a constant and e is the effective totaleccentricity signal for the complete set of rolls in the mill. S_(o) isnormally a constant however, on mills with oil film bearings, itincludes the effective rollgap position change induced by thebackup-roll bearing (a function of load and angular speed).

During rolling, the variations in roll force are typically less than 15percent of the average value and a linear model F/M, (for the non-linearfunction S(F,W) may be assumed and equation (1), in linearised formbecomes:

    ΔF=M(Δh-e-ΔS)                            (2)

where the mill modulus M is defined as ##EQU1##

The roll force F must also satisfy the nonlinear plastic deformationequation if inertial effects are negligible, that is:

    F=W P

where the specific roll force P is a function of h, rolling parametersand strip disturbances. The linear form of this equation is: ##EQU2##where F_(d) is a force change due to external disturbances other thanroll eccentricity.

Since the elastic and plastic deformation forces are always inequilibrium, solving equations (2) and (3) and eliminating ΔF gives:

    ΔS=(1+a)Δh-F.sub.d /M-e                        (4)

where ##EQU3##

This equation defines the control change required to achieve a specifiedthickness correction or to compensate for a known force disturbance.

Because of friction between the roll-neck bearings and the mill frame,and also in the cylinders of a hydraulic actuation mill, the measuredroll force F' may not be equal to the roll force F exerted on the stripby the work-rolls. Although the friction force may be less than 2percent of the average roll force, it can lead to significant errors inthe estimated thickness deviations. Assuming that the friction force isproportional to the applied force and has its direction determined bythe direction of the rollgap actuator, (i.e. Sign (S)), we may write anequation for the total friction force F_(f) as:

    F.sub.f μ.sub.f F'Sign(S)                               (5)

where μ_(f) is a constant friction factor and S is assumed to bepositive when the rollgap is opening. That is, the rolling force F isrelated to the measured force F' by the equation:

    F=F'-F.sub.f =[1-μ.sub.f Sign(S)]F'                     (6)

where the measured force is derived from a load cell placed between thehydraulic cylinder and the frame. Similar equations may be derived forother configurations of measurement and hysteresis models.

The estimate for the combined eccentricity and steady state offset e_(o)is obtained by substituting the above expression for roll force F inequation (1), that is:

(e+e₀)=h-(S-S₀)-S(F,W). (7)

Finally, to complete the process model formulation, a dynamic model forthe open-loop actuator response S, as a function of the input velocityreference signal S* is required. This may be written as:

    S=S*/s(1+sτ.sub.a), |S|≦S.sub.max (8)

where s denotes the Laplace transform variable. This means that theclosed loop, actuator position response will have the characteristics ofa second order system.

It may be assumed that mill modulus M, strip width W, the hysteresisforce coefficient μ_(f), and the time delay to the thickness gauge τ_(d)are known.

A known key concept in the control strategy is to use equation (7) toestimate the eccentricity and offset signal (e+e_(o)) directly fromprocess measurements, with the instantaneous thickness replaced by thedownstream thickness h' which corresponds to the exit thickness rolledat a time τ_(d) earlier where τ_(d) is the transport delay between therollgap and the thickness gauge. The time delay may be determined from aknowledge of the work roll speed or angular position and the nominalforward slip ratio which is defined as the product exit speed divided bythe work roll surface speed. The forward slip ratio may be calculatedfrom well-known equations as a function of product dimensions andproperties and nominal processing conditions. Thus, past values of S andF' must be stored so that (e+e₀) at time (t-τ_(d)) can be estimated as

    (e+e.sub.0).sub.t-τ.sbsb.d =h'.sub.t +S(F.sub.t-τ.sbsb.d,W)-(S.sub.t-τ.sbsb.d -S.sub.0) (9)

If the eccentricity signal has period τ, then we can estimate thecurrent value of (e+e_(o))_(t) as:

    (e+e.sub.0).sub.t =(e+e.sub.0).sub.t-τ                 (10)

Finally, we can again use equation (7) to give an instantaneous estimateof the strip exit thickness as:

    h.sub.t =S(F.sub.t, W)+(S.sub.t -S.sub.0)+(e+e.sub.0).sub.t (11)

where (e+e_(o)) is obtained from (9) and (10).

Equations (9) to (11) will be referred to as the "eccentricitycompensated" thickness estimator and desirably include additionalcompensation terms for hysteresis and eccentricity. If the response timeof the thickness gauge is appreciable, then appropriate filters can beintroduced to compensate measured force and rollgap position.

Numerous combinations of loop design could be considered to exploit theavailability of the thickness estimate h. Even the simplest system,consisting of a single loop controller with an input of h and an outputto the actuator speed reference S* gave excellent results. Furtherimprovement was achieved with three separate feedback loops for actuatorposition control, fast thickness estimate h control, and slower actingintegral control of the measured thickness h'. (See FIG. 3.)

Combining the outputs of the two outer loops yields a signal Δh*, whichrepresents the desired change in strip thickness:

    Δh*=k.sub.1 (h*-h)+k.sub.2∫ (h*-h')dt           (12)

where k₁, and k₂ are tuning constants and h* is the reference thickness.This is converted to a rollgap position change by multiplying by thefactor (1+a) derived in equation (4). This calculation is implemented bybox 20. To this a further predictive term [(e+e₀ )-(e-e₀)] may be addedto give a rollgap position reference S* which takes account of futureeccentricity signals and their effect on the gap between the work-rolls.Therefore the control equation for S* becomes:

    S*=(1+a)[k.sub.1 (h*-h)+k.sub.2 ∫(h*-h')dt]+[(e+e.sub.0)-(e+e.sub.0)]+S*.sub.0       (13)

where S*_(o) is the initial rollgap position when control is initiatedat the beginning of a coil. That is, referring to FIG. 3, ##EQU4##

Compensation for actuator non-linearity may be necessary to preventovershoot in response to large amplitude disturbances. This is due tointegrator operation when the actuator speed is constrained to itsmaximum value. Alternatively, different controller algorithms C_(i) maybe introduced.

The controller gain k₂ is mill speed dependent and should be varied as anon-linear function of the ratio (τ_(a) /τ_(d)). This function is bestdetermined by simulation, however, if the actuator response issufficiently fast, such that τ_(a) /τ_(d) is always less than 0.3, thenk₂ may be represented by a linear function of speed.

The previous sections have described the prediction of the eccentricitysignal in a purely deterministic. environment and when there is only onefundamental roll period in the eccentricity signal. In practice, allmeasurements will be corrupted by noise and therefore we are concernedwith the prediction of a periodic signal from noisy measurements. It hasbeen shown that a suitable prediction for the filtered estimate E_(t)may have the form:

    E.sub.t =αE.sub.t-τ +(1-α)(e+e.sub.0).sub.t, 0≦α≦1                                 (15)

Inspection of equation (15) shows that past data is given an exponentialweighting in forming the predicted estimate. The parameter α affects thememory of the filter such that if α is near 1 then the filter will havea long memory, good noise discrimination and a slow response to dynamicchanges in the eccentricity waveform. Conversely, if α is near 0 thefilter will have a short memory with poor noise discrimination but rapidadaptability. Thus the choice of α is a compromise between speed ofresponse and noise immunity. A fixed value of α was found to be adequatefor the the majority of rolling mill applications. If necessary, itcould be varied in response to a suitable signal characteristic.

When there are multiple eccentric rolls with different periods aseparate eccentricity estimator E, similar to that described previously,must be introduced for each of the m sets of rolls having distinctperiods.

The algorithms for each of the filters may be processed in any order.The input signal to each filter should preferably be calculated from theeccentricity signal, as determined by equation 7, minus the cumulativesum of the previously processed filters. That is, for filter number i,the input is: ##EQU5##

When forming the estimate E_(t), of the correct value of the compositeeccentricity signal for all rolls, the individual outputs of each filtermust be combined with appropriate synchronisation. That is, ##EQU6##

This is shown diagrammatically in FIG. 5 for the case of four differentperiod rolls.

The availability of an accurate, measured thickness reading for theestimation of the eccentricity signal ensures that errors in the elasticdeformation and hysteresis models are corrected by internal feedbackwithin the estimation algorithms. That is, in the "steady state", theestimated thickness h is equal to the measured thickness h' at allsample points on the eccentricity function. This leads to a remarkablerobustness property which reduces the dependence of the eccentricitycompensation performance upon assumed nominal model parameters. Ofcourse, the accuracy of the elastic deformation model does influencesthe disturbance attenuation properties of the h control loop. The steadystate error attenuation factor β of this loop in isolation may be shownto be a function of the controller gain k₁ and the mill modulusestimate, M: ##EQU7## where ε=(1-M/M)

Simulation results, presented hereinafter, confirmed that, if thevarious control loops which contain product dependent gains arecompensated using equation (13), then it is feasible to maintain a fast,consistent response over a wide range of rolled products.

The previous section discussed the steady state sensitivity of thecontrol law to model errors. Clearly, the transient performance dependsupon all parameters in the model, especially M, a, τ, and τ_(d). Theparameter M is a property of the mill and strip width and can reasonablybe assumed to be known within 10%. The time delay τ_(d) can beaccurately calculated from the instantaneous work-roll velocitymeasurements and the distance from the stand to the thickness measuringgauge. A good initial estimate for τ can be obtained in a similar way byusing the nominal diameter of the backup-rolls and forward slip ratio.However, this can be refined, if desired, by substituting τ for τ whereτ is defined as: ##EQU8## The appropriate value for τ₀ and the frequencyof updating τ will depend on the particular application in a similarmannner to α. Updating of τ should be avoided if the eccentricity signalis small or the mill speed is varying.

Finally, the parameter a can vary from coil to coil depending on rollingconditions and the material grade. The simulation tests indicated a highdegree of insensitivity to this parameter, however, if desired, it canbe determined from an adaptive model during the rolling of each coil.

FIG. 4 illustrates the estimation of the period under noisy conditions.Results such as these suggested that the estimated period should beestimated with an accuracy of better than 2%, provided that a sufficientnumber of samples is obtained during each roll revolution.

An extensive simulation evaluation of the new design performance hasbeen completed whose aim was to observe the controller performance underideal and non-ideal conditions. In the ideal case, when all relevantparameters are assumed known, the effect of roll-eccentricity on thestrip exit thickness can be eliminated, provided that the eccentricitydisturbances is within the capability of the rollgap positioning system.In the non-ideal case, when parameters are not equal to their truevalues, it has been found that the design exhibited a high degree ofrobustness.

A range of simulated responses are provided in FIGS. 6 and 7 toillustrate typical behaviour and the robustness of the control system toparameter variations for a fast rollgap actuator capable of respondingto a 0.1 mm rollgap change in 0.06 s. Signals are identified in FIG. 3.Key simulation parameters were:

    ______________________________________                                        *mill modulus: 3.5 MN/mm                                                      *strip width:  1000 mm                                                        *plasticity constant:                                                                        2.0                                                            *time delay:   0.4 s                                                          *control gains:                                                                              k.sub.1 = .sup.4, k.sub.2 = 1.0 s.sup.-1, τ.sub.f =                       0.25 s                                                         ______________________________________                                    

FIG. 6, presents typical simulation results for a composite inputthickness disturbance consisting of a step followed by a negative rampchange and then a harmonic signal with a period 1.5 times the stand 1backup-roll period. The periodic backup-roll eccentricity signal iscomprised of a first and third harmonic each of 0.04 mm peak to peakamplitude. For the nominal conditions shown above the attenuation factorβ is equal to 5.0 and this may be discerned from the step responsecomponents of the simulated thickness behaviour. The effectiveness ofthe eccentricity compensator is evident from a comparison of theresponse with and without the eccentricity compensator.

FIG. 7 shows results corresponding to FIG. 6 for the case whereparameter values are not equal to their nominal values. Specific resultsare provided for the case of a mill modulus error of 15% and aplasticity parameter of 3.0 (nominal value was 2.0).

FIG. 8 shows controller simulation results for the case of fourdifferent roll diameters in a four-high mill, each roll containing asimilar eccentricity amplitude.

Results have been obtained from the implementation of the recommendedcontrol system on a tandem cold mill having an electro-hydraulicposition control system which is comparatively slow by modern standards.(Step response time for a 0.1 mm change in rollgap position is 0.5 s.)The slow positioning system precludes effective dynamic cancellation ofthe eccentricity disturbance when the mill is rolling at full speed.However, at a reduced speed, improved performance resulted from thecombined operation of the eccentricity compensator and gaugemetercontroller as is evident in FIG. 9.

As will be evident to those skilled in the art, the invention hereindescribed may be adapted to different configurations of mill and toemploy control algorithms other than herein exemplified and suchmodified embodiments are deemed to be within the scope hereof.

We claim:
 1. A method for automatically controlling the thickness of product emerging from a rolling stand comprising the steps of producing a first input signal indicative of total roll force, producing a second input signal indicative of rollgap position, producing a third input signal indicative of the angular position of a first mill roll, producing a fourth input signal indicative of product thickness at a predetermined downstream location relative to the rollgap, and deriving from said first, second, third and fourth input signals a first output signal indicative of the total roll eccentricity affecting the true instantaneous rollgap position as a function of the first mill roll angular position.
 2. A method according to claim 1 wherein the rolling stand has a set of rolls with a common period of rotation which is directly related to the period of the first mill roll and comprising the step of filtering the first output so as to produce a second output indicative of the periodic roll eccentricity of the set of rolls.
 3. A method according to claim 2 wherein the rolling stand comprises a plurality of sets of rolls, each set comprising rolls sharing a common period, said method comprising the steps of producing a plurality of third input signals each indicative of roll angular position of one roll of a set,using each third signal of said plurality to filter the first output signal to produce a plurality of filtered output signals, and combining each filter output signal with the second output signal to produce a plurality of output signals each representing the periodic roll eccentricity of one of said plurality of sets.
 4. A method according to claim 1 wherein an input signal indicative of angular position of a roll is obtained by the step of integrating a signal indicative of roll angular speed.
 5. A method according to claim 1 further comprising the steps of filtering the first output signal to produce an output signal indicative of the period of rotation of a set of rolls sharing a common period.
 6. A method according to claim 3 and further comprising the step of adding together with appropriate synchronization the output signals representing the periodic roll eccentricities of said plurality of sets of rolls to produce a third output signal representing the predicted value of composite roll eccentricity at the roll gap corresponding to multiple sets of rolls having distinct periods.
 7. A method according to claim 1 further comprising the steps of combining the first and second input signals to produce a fourth output signal representing an estimate of the instantaneous thickness of product emerging from the rollgap, and producing a fifth output signal by compensating the fourth output signal for the roll eccentricity of one set of rolls indicated by the second output signal.
 8. A method according to claim 7 in which the fifth output signal is produced by compensating the fourth output signal with the roll eccentricity for multiple sets of rolls as indicated by the third output signal.
 9. A method according to claim 8 further comprising the steps of controlling the gap between the work rolls in accordance with the fifth output signal.
 10. A method according to claim 9 further including the step of compensating the first output signal for the effect of friction induced hysteresis between the rolling mill stand components.
 11. A method according to claim 6 further including the step of controlling the gap between the work rolls in accordance with the third output signal representing the predicted composite roll eccentricity signal.
 12. Apparatus for controlling the thickness of material produced by a rolling mill stand comprisingmeans for producing a first input signal indicative of roll force (F'), means for producing a second input signal indicative of rollgap position (S), means for producing a third input signal indicative of roll angular position, means for producing a fourth input signal indicative of product thickness at a predetermined position downstream relative to the rollgap (h), means for deriving from the first, second, third and fourth input signals a first output signal indicative of total roll eccentricity, means for coupling the means for producing the first, second, third and fourth input signals to the means for deriving from the first, second, third and fourth input signals an output signal, means for deriving a signal indicative of instantaneous product thickness at the rollgap, means for compensating the signal indicative of instantaneous product thickness for the total roll eccentricities indicated by the first output signal, means for coupling the means for deriving a signal indicative of instantaneous product thickness at the rollgap to the means for compensating the signal indicative of instantaneous product thickness for the total roll eccentricities indicated by the first output signal, and means for coupling the means for deriving from the first, second, third and fourth input signals a first output signal indicative of total roll eccentricity to the means for compensating the signal indicative of instantaneous product thickness for the total roll eccentricities indicated by the first output signal.
 13. Apparatus according to claim 12 further comprising means for controlling the gap between the work rolls in accordance with the compensated signal, andmeans for coupling the means for.controlling the gap between the work rolls in accordance with the compensated signal to the means for compensating the signal indicative of instantaneous product thickness for the total roll eccentricities indicated by the first output signal.
 14. Apparatus according to claim 12 further comprising means for deriving a signal indicative of instantaneous product thickness from the first input signal and the second input signal,means for coupling the means for deriving a signal indicative of instantaneous product thickness from the first input signal and the second input signal to the means for producing a first input signal and to the means for producing a second input signal, and means for coupling the means for deriving a signal indicative of instantaneous product thickness from the first input signal and the second input signal to the means for compensating the signal indicative of instantaneous product thickness for the total roll eccentricities indicated by the first output signal.
 15. Apparatus for controlling the thickness of material produced by a rolling mill stand comprisingmeans for producing a first input signal indicative of the roll force (F'), means for producing a second input signal indicative of rollgap position (S), means for producing a third input signal indicative of roll angular position, means for producing a fourth input signal indicative of product thickness at a predetermined downstream position relative to the rollgap (h), means for deriving from the first, second, third and fourth input signals a first output signal indicative of total roll eccentricities, means for coupling the means for producing the first, second, third and fourth input signals to the means for deriving from the first, second, third and fourth input signals a first output signal indicative of total roll eccentricities, means for filtering the first output signal to minimize the influence of noise and produce a second output signal representing the predicted, composite roll eccentricity at the rollgap for all rolls whose periods are specified by angular position or speed measurements or roll diameter information, means for coupling the means for deriving from the first, second, third and fourth input signals a first output signal indicative of total roll eccentricities to the means for filtering the first output signal, means for deriving from the first input signal and second input signal a third output signal indicative of instantaneous product thickness at the rollgap, means for coupling the means for producing a first input signal and the means for producing a second input signal to the means for deriving from the first input signal and second input signal a third output signal indicative of instantaneous product thickness at the rollgap, means for utilizing the second output signal and third output signal to adjust the rollgap position whereby to control thickness independently of roll eccentricity disturbances, and means for coupling the means for filtering the first output signal to minimize the influence of noise and produce a second output signal and the means for deriving from the first input signal and second input signal a third output signal indicative of instantaneous product thickness at the rollgap to the means for utilizing the second output signal and third output signal to adjust the rollgap position.
 16. Apparatus according to claim 15 wherein the means for coupling the means for deriving from the first input signal and second input signal a third output signal indicative of instantaneous product thickness at the rollgap to the means for utilizing the second output signal and third output signal to adjust the rollgap position comprises means for introducing a deadzone to reduce the effect of unfiltered error components in the instantaneous thickness estimate.
 17. A rolling mill comprising means for producing a first input signal indicative of total roll force, means for producing a second input signal indicative of rollgap position, means for producing a third signal indicative of the angular position of a first mill roll, means for producing a fourth input signal indicative of product thickness at a predetermined downstream location relative to the rollgap, and means for deriving from said first, second, third and fourth input signals a first output signal indicative of the total roll eccentricity affecting the true instantaneous rollgap position as a function of the first mill roll angular position, and means for coupling the first input signal producing means, the second input signal producing means, the third input signal producing means and the fourth input signal producing means to the means for deriving from said first, second, third and fourth input signals a first output signal.
 18. A rolling mill comprising apparatus for controlling the thickness of material produced thereby, said apparatus including means for producing a first input signal indicative of roll force (F'), means for producing a second input signal indicative of rollgap position (S), means for producing a third input signal indicative of roll angular position, means for producing a fourth input signal indicative of product thickness at a predetermined position downstream relative to the rollgap (h), means for deriving from the first, second, third and fourth input signals a first output signal indicative of total roll eccentricity, means for deriving a signal indicative of instantaneous product thickness at the rollgap, means for compensating the signal indicative of instantaneous product thickness for the total roll eccentricities indicated by the first output signal, means for coupling the first input signal producing means, the second input signal producing means, the third input signal producing means and the fourth input signal producing means to the means for deriving from the first, second, third and fourth input signals a first output signal, means for coupling the means for deriving a signal indicative of instantaneous product thickness at the rollgap to the means for compensating the signal indicative of instantaneous product thickness, and means for coupling the means for deriving from the first, second, third and fourth input signals of first output signal to the means for compensating the signal indicative of instantaneous product thickness. 